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General Certificate of Secondary Education
Higher Tier
June 2015
Applications of Mathematics
(Linked Pair)
93702H
H
1.30 pm to 3.00 pm
a calculator

mathematical instruments.
4–5
6–7
8–9
12 – 13
14 – 15
16 – 17
For this paper you must have:

3
10 – 11
Unit 2 Geometry and Measures
Thursday 11 June 2015
Mark
18 – 19
20 – 21
22 – 23
Time allowed
 1 hour 30 minutes
24 – 25
Instructions
 Use black ink or black ball-point pen. Draw diagrams in pencil.
 Fill in the boxes at the top of this page.
 Answer all questions.
 You must answer the questions in the spaces provided. Do not write outside
the box around each page or on blank pages.
 Do all rough work in this book. Cross through any work that you do not want
to be marked.
 If your calculator does not have a π button, take the value of π to be
3.14 unless another value is given in the question.
26 – 27
28 – 29
TOTAL
Information
The marks for questions are shown in brackets.
 The maximum mark for this paper is 80
 The quality of your written communication is specifically assessed
in Questions 2 and 19
These questions are indicated with an asterisk (*).
 You may ask for more answer paper, graph paper and tracing paper.
These must be tagged securely to this answer book.
 You are expected to use a calculator where appropriate.

Advice
 In all calculations, show clearly how you work out your answer.
(JUN1593702H01)
WMP/Jun15/93702H/E5
93702H
2
Formulae Sheet: Higher Tier
a
1
Area of trapezium = –
(a + b)h
h
2
b
Volume of prism = area of cross section × length
cross
section
h
lengt
r
4
πr3
Volume of sphere = –
3
Surface area of sphere = 4 π r 2
1
Volume of cone = –
π r2h
l
3
h
Curved surface area of cone = π rl
r
In any triangle ABC
C
Area of triangle =
1
–
2
ab sin C
a
b
b
a
c
Sine rule ––––– = ––––– = –––––
sin A
sin B
sin C
A
c
B
Cosine rule a2 = b2 + c2 – 2bc cos A
The Quadratic Equation
The solutions of ax2 + bx + c = 0, where a ≠ 0, are given by
– b ± √ (b2 – 4ac)
–––––––––––––––
x=
2a
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Answer all questions in the spaces provided.
1
To make pancakes for 6 people you need 210 millilitres of milk.
How much milk do you need to make pancakes for 4 people?
[2 marks]
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Answer .................................................................. ml
Turn over for the next question
2
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4
2
Saj has four bags of apples.
A
B
C
D
x apples
(x + 6) apples
5x apples
2(x + 6) apples
Bag C and Bag D have the same number of apples.
2 (a)
Circle the correct equation.
[1 mark]
............................................................................................................................................
............................................................................................................................................
5x = 2x + 6
2 (b)
5x = 2x + 12
2x = 5x – 6
5x = x + 12
Work out the number of apples in bag A.
[2 marks]
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Answer ......................................................................
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*2 (c)
Saj needs 5 apples to make an apple pie.
Are there enough apples in all four bags to make 10 apple pies?
You must show your working.
[2 marks]
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Turn over for the next question
5
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3
A rug is in the shape of a trapezium.
1.4 m
Not drawn
accurately
75 cm
1.8 m
Work out the area of the rug.
State the units of your answer.
[3 marks]
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Answer ......................................................................
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4
Numbers that are the product of two different prime numbers are used in internet
security.
6497 is the product of two prime numbers.
4 (a)
Explain why
one of the prime numbers could have unit digit 3
and
the other prime number could have unit digit 9
[1 mark]
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4 (b)
Work out the two prime numbers which have a product of 6497
[2 marks]
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Answer ....................... and .......................
6
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8
5
The scale drawing shows the positions of towns A, B, C and D.
Scale
1 cm represents 5 km
North
B
A
C
5 (a)
D
A helicopter flies directly from A to C.
On what bearing does the helicopter fly?
[1 mark]
Answer .................................................................... º
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9
5 (b)
The distances along roads between the towns are shown in this table, in kilometres.
A
A
B
C
D
52
59
36
38
54
B
52
C
59
38
D
36
54
39
39
A car travels by road
from A to D
and then from D to C.
How many more kilometres does the car travel than the helicopter?
[3 marks]
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Answer ................................................................. km
4
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10
6
Four containers are of equal height.
These diagrams show the cross section of each container.
A
B
C
D
Water flows into each container at a constant rate until the container is full.
These sketch graphs show how the depth of the water changes with time, for each
container.
Graph 1
Depth
Depth
Time
Time
Graph 3
Graph 4
Depth
Depth
Time
(10)
Graph 2
Time
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6 (a)
Complete this table to match each container to a graph.
[2 marks]
6 (b)
Container A
Graph ............
Container B
Graph ............
Container C
Graph ............
Container D
Graph ............
Which graph shows that the depth of water increases at a constant rate until the
container is full?
[1 mark]
Answer ......................................................................
Turn over for the next question
3
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12
7
A company designs and prints standard and exclusive wedding invitation cards.
This graph shows how much the company charges for up to 100 exclusive cards.
Exclusive
110
100
90
80
70
Charge (£)
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
Number of cards
This table shows the design and printing charges for the standard card.
7 (a)
(12)
Design
charge
Printing
charge
£40
30p per card
On the grid above, draw a graph to show how much the company charges for up to 100
standard cards.
[2 marks]
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13
7 (b)
Work out the total charge for 10 exclusive cards and 50 standard cards.
[2 marks]
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Answer £ ...................................................................
7 (c)
Ann and Mike want to spend £130 on wedding invitation cards.
They would like 150 exclusive cards.
Is £130 enough?
You must show your working.
[2 marks]
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Turn over for the next question
6
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14
8
A ship travels a distance of 30 km at a speed of 24 km/h
Work out the time taken.
Give your answer in hours and minutes.
[3 marks]
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Answer ................... hours ................... minutes
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9
You will need a ruler and compasses to answer this question.
The scale drawing shows the positions of three trees, P, Q and R on an island.
Scale
1 cm represents 100 metres
P
R
Q
Some treasure is buried
less than 500 metres from P
less than 750 metres from R
nearer to P than to Q.
Shade the region where the treasure could be.
[3 marks]
6
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16
10
Jack sells packs of envelopes.
There are three types of pack, Economy (E), Standard (S) and Luxury (L).
One week he sells 270 packs in the ratio
E:S:L=5:3:2
He makes a profit of
12p a pack on Economy packs
15p a pack on Standard packs
20p a pack on Luxury packs.
Work out the total profit he makes selling envelopes.
[3 marks]
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Answer £ ...................................................................
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11
1
The diagram shows a section of a railway line with gradient ––
37
Not drawn
accurately
x metres
a
200 metres
11 (a)
Work out the value of x.
Give your answer to 3 significant figures.
[3 marks]
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Answer .......................................................................
11 (b)
Work out the size of angle a.
[3 marks]
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Answer ........................................................ degrees
9
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18
12
The depth of water in a harbour is modelled by the equation
d = 7 + 2 sin (30t)º
d is the depth of water in metres.
t is the number of hours after 4.00 am
The graph shows the depth of water for values of t from 0 to 6
d
10
9
8
7
6
5
4
3
2
1
0
0
(18)
1
2
3
4
5
6
7
8
9
10
11
12
t
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19
12 (a)
Complete the table.
[2 marks]
t
7
8
9
10
11
12
d
12 (b)
On the grid opposite, draw the graph for values of t from 6 to 12
[1 mark]
12 (c)
Between what times of day is the depth at least 8 metres?
[2 marks]
Between ........................ and ........................
Turn over for the next question
5
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20
13
John makes a square tile ABCD.
He joins together
quadrilateral AOCD
isosceles triangle BOC
triangle AOB.
OB = CB
A
B
Not drawn
accurately
O
15º
D
C
Show that triangle AOB is equilateral.
You must show your working, some of which may be on the diagram.
[5 marks]
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21
14
The diagram shows a paperweight.
The paperweight is made from these two similar glass cylinders.
2 cm
3 cm
5 cm
The density of the glass is 2.6 g per cm3
Work out the mass of the paperweight in grams.
[5 marks]
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Answer ................................................................... g
10
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22
15
Chloe is training for a marathon.
These speed-time graphs model her training runs on Monday and Wednesday.
Monday
250
200
Speed
150
(metres/min)
100
50
0
0
5
10
15
20
25
30
35
40
45
50
55
60
40
45
50
55
60
Time (min)
Wednesday
250
200
Speed
150
(metres/min)
100
50
0
0
5
10
15
20
25
30
35
Time (min)
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23
On which day did Chloe run further?
You must show your working.
[4 marks]
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Answer ......................................................................
4
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24
16
The shaded section ABC shows the plan view of a silver pendant.
OAB is a sector of a circle, centre O, radius 95 mm
B
C
A
Not drawn
accurately
95 mm
95 mm
45°
O
16 (a)
Work out the area of the sector OAB.
[3 marks]
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Answer .............................................................. mm2
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16 (b)
Show that OC = 67.2 mm to 3 significant figures.
[2 marks]
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16 (c)
The silver pendant is a prism with thickness 2.5 mm
The cross section is shown.
B
C
Not drawn
accurately
A
Work out the volume of silver in the pendant.
[3 marks]
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Answer .............................................................. mm3
8
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26
17
A hanging basket consists of
a hemisphere of diameter 24 cm
3 chains, OA, OB and OC, each of length 28 cm
A, B and C are 3 points on the circular rim of the hemisphere.
O is directly above X, the centre of circle ABC.
O
A
C
X
B
Work out the length OX.
[3 marks]
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Answer ................................................................. cm
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27
18
For a model aeroplane
L = length in centimetres
A = surface area of the wings in square centimetres
M = mass in grams
A model aeroplane has
L = 24
A = 120
M = 40
A larger, similar model aeroplane is made by increasing the length by scale factor x.
18 (a)
Circle the expression for the surface area of the wings of the larger model.
[1 mark]
24x
18 (b)
24x2
120x
120x2
30x2
Circle the expression for the mass of the larger model.
[1 mark]
40x
18 (c)
40x2
For a model aeroplane to fly
40x3
M÷A
24x3
120x
must be 0.5 or less.
Work out the biggest value that x can be for the larger model to fly.
[2 marks]
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Answer ......................................................................
7
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28
*19
The distance-time graph shows a car journey on a motorway.
Distances are measured in kilometres.
60
50
Distance
(kilometres)
40
30
20
10
0
9.00
9.10
9.20
9.30
9.40
Time of day (am)
The speed limit for the motorway is 70 miles per hour.
At 9.20 am, was the car travelling at more than 70 miles per hour?
You must show your working.
[5 marks]
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END OF QUESTIONS
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